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Integral Calculus

Blazing goIITian

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1 Apr 2009 07:34:56 IST

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288

differential eqns.....

None

the order of the diff. eqn whose general soln is given by y = ( C1 + C2) cos ( x + C3) + C4 e^ ( x + C5 ) where all C's are constants...is...

1) 5

2) 4

3) 3

4) 2

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Comments (8)

Angshuman Bharadwaz

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1 Apr 2009 19:28:33 IST

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The answer is :- Order 2Because.... If you double differentiate the general solution then the differential equation comes out to be y'' + y' = 0Don't forget to rate my answer!!!!!

Shubhat aka Shubbhuu

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1 Apr 2009 19:33:05 IST

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No the answer is not order 2 because there are four independent constants (c1+c2), c3, c4, c5 in the equation.

The answer is order 4.

Angshuman Bharadwaz

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1 Apr 2009 19:44:21 IST

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Oh sorry ,,,,its my mistake the order is 4......very sorry....thanks Subhat....

shubham sunder

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1 Apr 2009 22:40:58 IST

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the order given was 3.....didn't understand why???

pranav agrawal

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1 Apr 2009 22:46:30 IST

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wait i explain~

Mirka

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1 Apr 2009 22:47:52 IST

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given Eqn :: y = ( C1 + C2) cos ( x + C3) + C4 e^ ( x + C5 )

y = ( C1 + C2) cos ( x + C3) + C4 (e^ x * e ^ C5 )

y = A cos ( x + B ) + C4 * e^ C5 * e^x

so,

y = A cos ( x + B ) + C * e^x

wer A, B, C are constants { A = C1 + C2 , B = c3 and C = c4 * e ^ C5 }

so, there are 3 constants

hence, order = 3

shubham sunder

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1 Apr 2009 22:50:37 IST

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thnxx....

pranav agrawal

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1 Apr 2009 22:50:45 IST

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y = ( C1 + C2) cos ( x + C3) + C4 e^ ( x + C5 )

dy / dx = - ( C1 + C2) sin ( x + C3) + C4 e^ ( x + C5 )

d2y / dx2 = - ( C1 + C2) cos ( x + C3) + C4 e^ ( x + C5 )

d3y / dx3 = ( C1 + C2) sin ( x + C3) + C4 e^ ( x + C5 )

now ,

d3y / dx3 + d2y / dx2 - ( dy / dx + y) = 0

or,

d3y / dx3 + d2y / dx2 - dy / dx - y = 0

this is a differantial equation in x whose order is 3 and degree 1

hope you got now~

do rate~~

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